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PHXII08:ELECTROMAGNETIC WAVES

368923 A parallel plate capacitor consists of two circular plates of radius $0.1 m$ . They are separated by a distance $0.5 m m$ . If electric field between the capacitor plates changes as $\frac{d E}{d t} = 5 \times 10^{13} \frac{V}{m \times s}$ find displacement current between the plates.

1

10.9 A

2

11.9 A

3

12.9 A

4

13.9 A

Explanation:

Area of plates $A = π r^{2} = 3.14 \times (0.1)^{2} m^{2}$
$\frac{d E}{d t} = 5 \times 10^{3} \frac{V}{m \times s}$
$1_{d} = ε_{0} A [\frac{d E}{d t}] {∵ \frac{d ϕ_{E}}{d t} = A \frac{d E}{d t}}$
$= 8.85 \times 10^{- 12} \frac{C^{2}}{N m^{2}} \times 3.14 \times (0.1)^{2} m^{2} \times 5 \times 10^{13} \frac{V}{m \times s}$
$1_{d} = 13.9 A$

PHXII08:ELECTROMAGNETIC WAVES

368924 The charge on a parallel plate capacitor is varying as $q = q_{0} \sin 2 π n t$ The plates are very large and close to each other. Neglecting the edge effects, the displacement current through the capacitor is

1

\frac{q}{ε_{0} A}

2

\frac{q_{0}}{ε_{0}} \sin 2 π n t

3

2 π n q_{0} \cos 2 π n t

4

\frac{2 π n q_{0}}{ε} \cos 2 π n t

Explanation:

$I_{D} = \frac{d q}{d t} = \frac{d}{d t} q_{0} \sin 2 π n t = 2 π n q_{0} \cos 2 π n t$

PHXII08:ELECTROMAGNETIC WAVES

368925 The displacement current flows in the dielectric of a capacitor when the potential difference across its plate

1 Is changing with time

2 Displacement current does not depend on potential difference

3 Becomes zero

4 Has assumed a constant value

Explanation:

$i_{d} = ε_{0} \frac{d ϕ}{dt} = ε_{0} \frac{Ad E}{dt}$
$\Rightarrow i_{d} \neq 0 whenever \frac{d E}{dt} \neq 0$

PHXII08:ELECTROMAGNETIC WAVES

368926 A parallel plate capacitor is charged by connecting it to a battery through a resistor. If $I$ is the current in the circuit, then in the gap between the plates:

1 There is no current

2 Displacement current of magnitude equal to

I

flows in the same direction as

I

3 Displacement current of magnitude equal to

I

flows in a direction opposite to that of

I

4 Displacement current of magnitude greater than I flows but can be in any direction

Explanation:

From modified Ampere's law
$\oint B . d l = μ_{0} (I_{C} + I_{D})$
supporting img
For Loop $L_{1} I_{C} \neq 0$ and $I_{D} = 0$
For Loop $L_{2} I_{C} = 0$ and $I_{D} \neq 0$
Due to $K C L I_{C} = I_{D} = I$

NEET - 2024

PHXII08:ELECTROMAGNETIC WAVES

368923 A parallel plate capacitor consists of two circular plates of radius $0.1 m$ . They are separated by a distance $0.5 m m$ . If electric field between the capacitor plates changes as $\frac{d E}{d t} = 5 \times 10^{13} \frac{V}{m \times s}$ find displacement current between the plates.

1

10.9 A

2

11.9 A

3

12.9 A

4

13.9 A

Explanation:

Area of plates $A = π r^{2} = 3.14 \times (0.1)^{2} m^{2}$
$\frac{d E}{d t} = 5 \times 10^{3} \frac{V}{m \times s}$
$1_{d} = ε_{0} A [\frac{d E}{d t}] {∵ \frac{d ϕ_{E}}{d t} = A \frac{d E}{d t}}$
$= 8.85 \times 10^{- 12} \frac{C^{2}}{N m^{2}} \times 3.14 \times (0.1)^{2} m^{2} \times 5 \times 10^{13} \frac{V}{m \times s}$
$1_{d} = 13.9 A$

PHXII08:ELECTROMAGNETIC WAVES

368924 The charge on a parallel plate capacitor is varying as $q = q_{0} \sin 2 π n t$ The plates are very large and close to each other. Neglecting the edge effects, the displacement current through the capacitor is

1

\frac{q}{ε_{0} A}

2

\frac{q_{0}}{ε_{0}} \sin 2 π n t

3

2 π n q_{0} \cos 2 π n t

4

\frac{2 π n q_{0}}{ε} \cos 2 π n t

Explanation:

$I_{D} = \frac{d q}{d t} = \frac{d}{d t} q_{0} \sin 2 π n t = 2 π n q_{0} \cos 2 π n t$

PHXII08:ELECTROMAGNETIC WAVES

368925 The displacement current flows in the dielectric of a capacitor when the potential difference across its plate

1 Is changing with time

2 Displacement current does not depend on potential difference

3 Becomes zero

4 Has assumed a constant value

Explanation:

$i_{d} = ε_{0} \frac{d ϕ}{dt} = ε_{0} \frac{Ad E}{dt}$
$\Rightarrow i_{d} \neq 0 whenever \frac{d E}{dt} \neq 0$

PHXII08:ELECTROMAGNETIC WAVES

368926 A parallel plate capacitor is charged by connecting it to a battery through a resistor. If $I$ is the current in the circuit, then in the gap between the plates:

1 There is no current

2 Displacement current of magnitude equal to

I

flows in the same direction as

I

3 Displacement current of magnitude equal to

I

flows in a direction opposite to that of

I

4 Displacement current of magnitude greater than I flows but can be in any direction

Explanation:

From modified Ampere's law
$\oint B . d l = μ_{0} (I_{C} + I_{D})$
supporting img
For Loop $L_{1} I_{C} \neq 0$ and $I_{D} = 0$
For Loop $L_{2} I_{C} = 0$ and $I_{D} \neq 0$
Due to $K C L I_{C} = I_{D} = I$

NEET - 2024

PHXII08:ELECTROMAGNETIC WAVES

368923 A parallel plate capacitor consists of two circular plates of radius $0.1 m$ . They are separated by a distance $0.5 m m$ . If electric field between the capacitor plates changes as $\frac{d E}{d t} = 5 \times 10^{13} \frac{V}{m \times s}$ find displacement current between the plates.

1

10.9 A

2

11.9 A

3

12.9 A

4

13.9 A

Explanation:

Area of plates $A = π r^{2} = 3.14 \times (0.1)^{2} m^{2}$
$\frac{d E}{d t} = 5 \times 10^{3} \frac{V}{m \times s}$
$1_{d} = ε_{0} A [\frac{d E}{d t}] {∵ \frac{d ϕ_{E}}{d t} = A \frac{d E}{d t}}$
$= 8.85 \times 10^{- 12} \frac{C^{2}}{N m^{2}} \times 3.14 \times (0.1)^{2} m^{2} \times 5 \times 10^{13} \frac{V}{m \times s}$
$1_{d} = 13.9 A$

PHXII08:ELECTROMAGNETIC WAVES

368924 The charge on a parallel plate capacitor is varying as $q = q_{0} \sin 2 π n t$ The plates are very large and close to each other. Neglecting the edge effects, the displacement current through the capacitor is

1

\frac{q}{ε_{0} A}

2

\frac{q_{0}}{ε_{0}} \sin 2 π n t

3

2 π n q_{0} \cos 2 π n t

4

\frac{2 π n q_{0}}{ε} \cos 2 π n t

Explanation:

$I_{D} = \frac{d q}{d t} = \frac{d}{d t} q_{0} \sin 2 π n t = 2 π n q_{0} \cos 2 π n t$

PHXII08:ELECTROMAGNETIC WAVES

368925 The displacement current flows in the dielectric of a capacitor when the potential difference across its plate

1 Is changing with time

2 Displacement current does not depend on potential difference

3 Becomes zero

4 Has assumed a constant value

Explanation:

$i_{d} = ε_{0} \frac{d ϕ}{dt} = ε_{0} \frac{Ad E}{dt}$
$\Rightarrow i_{d} \neq 0 whenever \frac{d E}{dt} \neq 0$

PHXII08:ELECTROMAGNETIC WAVES

368926 A parallel plate capacitor is charged by connecting it to a battery through a resistor. If $I$ is the current in the circuit, then in the gap between the plates:

1 There is no current

2 Displacement current of magnitude equal to

I

flows in the same direction as

I

3 Displacement current of magnitude equal to

I

flows in a direction opposite to that of

I

4 Displacement current of magnitude greater than I flows but can be in any direction

Explanation:

From modified Ampere's law
$\oint B . d l = μ_{0} (I_{C} + I_{D})$
supporting img
For Loop $L_{1} I_{C} \neq 0$ and $I_{D} = 0$
For Loop $L_{2} I_{C} = 0$ and $I_{D} \neq 0$
Due to $K C L I_{C} = I_{D} = I$

NEET - 2024

PHXII08:ELECTROMAGNETIC WAVES

368923 A parallel plate capacitor consists of two circular plates of radius $0.1 m$ . They are separated by a distance $0.5 m m$ . If electric field between the capacitor plates changes as $\frac{d E}{d t} = 5 \times 10^{13} \frac{V}{m \times s}$ find displacement current between the plates.

1

10.9 A

2

11.9 A

3

12.9 A

4

13.9 A

Explanation:

Area of plates $A = π r^{2} = 3.14 \times (0.1)^{2} m^{2}$
$\frac{d E}{d t} = 5 \times 10^{3} \frac{V}{m \times s}$
$1_{d} = ε_{0} A [\frac{d E}{d t}] {∵ \frac{d ϕ_{E}}{d t} = A \frac{d E}{d t}}$
$= 8.85 \times 10^{- 12} \frac{C^{2}}{N m^{2}} \times 3.14 \times (0.1)^{2} m^{2} \times 5 \times 10^{13} \frac{V}{m \times s}$
$1_{d} = 13.9 A$

PHXII08:ELECTROMAGNETIC WAVES

368924 The charge on a parallel plate capacitor is varying as $q = q_{0} \sin 2 π n t$ The plates are very large and close to each other. Neglecting the edge effects, the displacement current through the capacitor is

1

\frac{q}{ε_{0} A}

2

\frac{q_{0}}{ε_{0}} \sin 2 π n t

3

2 π n q_{0} \cos 2 π n t

4

\frac{2 π n q_{0}}{ε} \cos 2 π n t

Explanation:

$I_{D} = \frac{d q}{d t} = \frac{d}{d t} q_{0} \sin 2 π n t = 2 π n q_{0} \cos 2 π n t$

PHXII08:ELECTROMAGNETIC WAVES

368925 The displacement current flows in the dielectric of a capacitor when the potential difference across its plate

1 Is changing with time

2 Displacement current does not depend on potential difference

3 Becomes zero

4 Has assumed a constant value

Explanation:

$i_{d} = ε_{0} \frac{d ϕ}{dt} = ε_{0} \frac{Ad E}{dt}$
$\Rightarrow i_{d} \neq 0 whenever \frac{d E}{dt} \neq 0$

PHXII08:ELECTROMAGNETIC WAVES

368926 A parallel plate capacitor is charged by connecting it to a battery through a resistor. If $I$ is the current in the circuit, then in the gap between the plates:

1 There is no current

2 Displacement current of magnitude equal to

I

flows in the same direction as

I

3 Displacement current of magnitude equal to

I

flows in a direction opposite to that of

I

4 Displacement current of magnitude greater than I flows but can be in any direction

Explanation:

From modified Ampere's law
$\oint B . d l = μ_{0} (I_{C} + I_{D})$
supporting img
For Loop $L_{1} I_{C} \neq 0$ and $I_{D} = 0$
For Loop $L_{2} I_{C} = 0$ and $I_{D} \neq 0$
Due to $K C L I_{C} = I_{D} = I$

NEET - 2024